Re: Lists

• To: mathgroup at smc.vnet.net
• Subject: [mg46987] Re: Lists
• From: astanoff at yahoo.fr (astanoff)
• Date: Thu, 18 Mar 2004 04:38:03 -0500 (EST)
• References: <c3bgbb\$7pl\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Clément wrote:

> Hello MathGroup,

> I'm french so i don't speak english very well...

> I have resolved an equation. So i have a list of solutions.
> But how can i extract only the reel solutions of this list ?

> thanks

--
Clément,

Zis is ze way I do :

In[1]:=
realSolutions[sol_]:=#[[1]]&/@Select[{#,#//N}&/@sol,FreeQ[#[[2]],Complex]&];

Example (InputForms inserted for readability) :

In[2]:=sol=Solve[x^3-x+1 == 0];

In[3]:=sol//InputForm

Out[3]//InputForm=
{{x -> -(2/(3*(9 - Sqrt[69])))^(1/3) - ((9 - Sqrt[69])/2)^(1/3)/3^(2/3)},
{x -> ((1 + I*Sqrt[3])*((9 - Sqrt[69])/2)^(1/3))/(2*3^(2/3)) +
(1 - I*Sqrt[3])/(2^(2/3)*(3*(9 - Sqrt[69]))^(1/3))},
{x -> ((1 - I*Sqrt[3])*((9 - Sqrt[69])/2)^(1/3))/(2*3^(2/3)) +
(1 + I*Sqrt[3])/(2^(2/3)*(3*(9 - Sqrt[69]))^(1/3))}}

In[4]:=realSolutions[sol]//InputForm
Out[4]//InputForm=
{{x -> -(2/(3*(9 - Sqrt[69])))^(1/3) - ((9 - Sqrt[69])/2)^(1/3)/3^(2/3)}}

--
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```

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